A KINETIC-THEORY OF SUSPENSIONS

The Fokker-Planck formalism is used to construct a statistical-mechanical theory of the linear viscoelastic response of a colloidal dispersion of freely rotating spheres. It is assumed that the Newtonian solvent exerts random, fluctuating forces upon the solute spheres and systematic, frictional forces as well. The direct interactions among the spheres are separated into short-ranged, hard-core repulsions and longer-ranged, continuous forces. This model leads to a stress tensor for the suspension of the form sigma = sigma(SS) + sigma(PP) + 2-sigma(hy), with sigma(PP) denoting the contribution due to the translational motions of the suspended particles (P) and their mutual interactions. The term 2-sigma(hy) arises directly from the frictional, hydrodynamic interactions between the spheres and the solvent and sigma(SS) is the stress tensor of the (continuum) solvent perturbed by the presence of the solute spheres. Formulas are obtained for the linear viscoelastic moduli associated with sigma(PP) and sigma(hy) and explicit procedures are presented for computing the numerical values of these coefficients. The theory is equally applicable to concentrated and dilute suspensions and it clearly can be extended to solute particles with internal (rotational and/or vibrational) degrees of freedom.